Photonic apparatus, methods, and applications

ABSTRACT

An optical microtoroid resonator including one or more nanoparticles attached to a surface of the resonator and capable of receiving an input signal from afar-field source (via free-space transmission) and outputting light propagating within the optical apparatus. A method for coupling light into and out of an optical resonator using a nanoparticle or nanoparticles to interface with spatially separated far-field optical elements.

RELATED APPLICATION DATA

The instant application claims priority to U.S. Provisional applicationSer. 62/356,240 filed Jun. 29, 2016, the subject matter of which isincorporated by reference herein in its entirety.

GOVERNMENT FUNDING

N/A.

BACKGROUND

Aspects and embodiments of the invention are in the field of photonics;more particularly, photonic apparatus, methods, and applications; mostparticularly, photonic resonator apparatus incorporating nanoparticles,associated methods, and applications thereof.

Sensitive and portable sensors are desirable for a wide variety ofapplications including early disease diagnosis and prognosis, monitoringfood and water quality, as well as detecting bacteria and viruses forpublic health concerns. Frequency-locked microtoroid optical resonatorshave been shown to be extremely sensitive sensors capable of detectingindividual protein molecules at a concentration of one part in aquadrillion (0.001 pg/mL).

It would be beneficial and advantageous to miniaturize these sensors inorder to make them portable and easily translatable to otherlaboratories or the field. Currently, however, light is coupled intothese sensors using a tapered optical fiber (FIG. 1) that is lifted offof the substrate, requiring alignment with nanoscale precision relativeto the microtoroid resonator. The time-consuming fabrication andalignment of this tapered optical fiber is one of the main impedimentsto easy miniaturization and scalable manufacturing of microtoroidoptical resonator sensing systems.

It would thus be further beneficial and advantageous to have a photonicresonator apparatus that does not require an external waveguide (e.g.,tapered optical fiber) to couple light into and out of the resonator, aswell as methods and techniques to more easily manufacture such apparatushaving increased detection sensitivity, in larger quantities. A furtherincrease in sensitivity of these sensors would be useful for detectingeven smaller signals such as those that would be generated from smallermolecules than have been previously detected, or for detectingconformational changes within a single protein.

Summary and Non-limiting Discussion

An aspect of the invention is an optical apparatus capable of receivingan input signal from a far-field source (via free-space transmission)and outputting light propagating within the optical apparatus. Accordingto an exemplary embodiment, the apparatus consists of an opticalresonator including one or more nanoparticles attached to a surface ofthe resonator. According to various exemplary, non-limiting embodiments,the apparatus may additionally include one or more of the followingcomponents, assemblies, features, limitations or characteristics, aloneor in various combinations as one skilled in the art would understand:

wherein the one or more nanoparticles are plasmonic nanoparticles;

wherein the one or more nanoparticles is a high refractive indexdielectric or semiconductor;

wherein the one or more nanoparticles is at least one of Si, Ge, Te,GaAs;

characterized in that the optical apparatus operates as a label-freebiosensor;

characterized in that the optical apparatus operates as a singlemolecule detector;

wherein the one or more nanoparticles are non-spherical;

wherein the one or more non-spherical nanoparticles have a polarizationthat is aligned with a polarization of a light in the optical resonator;

wherein the one or more non-spherical nanoparticles have a bow-tiegeometry;

wherein the one or more nanoparticles are at least one of a nanoshell, agold nanosphere, a silver nanosphere, a nanorod, a nanoplate, and ametal-dielectric composite nanoshell;

wherein the optical resonator is characterized by a quality factor, Q,that is equal to or greater than 10⁵;

wherein the optical resonator is a silica microtoroid;

wherein the one or more nanoparticles are chemically attached to themicrotoroid;

wherein the one or more nanoparticles comprise a phased array ofnanoparticles;

wherein the one or more nanoparticles comprises a metasurface;

wherein the one or more nanoparticles comprise one or more groupings ofnanoparticles;

wherein assemblies of nanoparticles are used.

An aspect of the invention is a method for coupling light into and outof an optical resonator using a nanoparticle or nanoparticles tointerface with spatially separated far-field optical elements. Accordingto various exemplary, non-limiting embodiments, the method mayadditionally include one or more of the following steps, components,assemblies, features, limitations or characteristics, alone or invarious combinations as one skilled in the art would understand:

further comprising non-randomly attaching a nanoparticle to an opticalresonator comprising positioning and attaching a nanoparticle to adesired location within +0.5-100 nm along a surface of the resonator,wherein a hotspot of ultra-high electric field intensity (E_(w)/nano=10to 1000×E_(w)/o nano) is created within an evanescent zone of theresonator;

further comprising using one of an optical tweezer and an atomic forcemicroscope technique/apparatus or micronozzle to position and attach thenanoparticle to the desired location;

wherein the nanoparticle is a plasmonic nanoparticle;

wherein the nanoparticle is a high refractive index dielectric orsemiconductor;

wherein the nanoparticle is at least one of Si, Ge, Te, GaAs;

wherein the desired location is an equatorial (circumferential) regionof a microtoroid;

wherein the optical resonator is an optical micro-resonator;

further comprising positioning and attaching a maximum plurality ofnanoparticles to a respective plurality of desired locations (+0.5-100nm) along the surface of the resonator;

wherein the one or more nanoparticles are non-spherical, furthercomprising controlling the orientation of the non-spherical nanoparticleso as to align the particle's direction of maximum polarizability withthe polarization of a light in the optical resonator;

wherein the desired location is a known position that provides anoperational interface, which enables input/output of light to/from theresonator via an external element;

further comprising positioning and attaching at least one of ananoshell, a gold nanosphere, a silver nanosphere, a nanorod, ananoplate, and a metal-dielectric composite nanoshell;

further comprising using the optical resonator to detect a singlemolecule of an analyte;

further comprising using the optical resonator to detect a singleprotein molecule;

comprising chemically attaching the nanoparticle to the resonator;

further comprising coating the nanoparticle with streptavidin; andcovalently binding a silane-PEG-biotin linker to the resonator surface;

further comprising attaching the nanoparticle to the resonator via atleast one of covalent bonding; chemisorption; and noncovalentinteractions.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1: Schematic top perspective view showing how light is coupled intoa microtoroid optical resonator from an optical fiber, as known in theart.

FIG. 2: A microtoroid is an example of a whispering gallery mode opticalresonator. FIG. 2A) A scanning electron micrograph of a microtoroid;FIG. 2B) A schematic of the evanescent wavefront interacting withmolecules near the microtoroid (not to scale); FIG. 2C) Graphicalrepresentation showing that molecules binding to the toroid's surfacechange the resonant frequency of the device, according to illustrativeembodiments of the invention.

FIG. 3 is a finite element COMSOL simulation of the capacitive Poyntingenergy density inside a silica microtoroid with major and minordiameters of 90 and 4 microns, respectively. The view presented is of across-section of the microtoroid. The toroid is immersed in water. Partof the electric field evanesces beyond the rim of the microtoroid (solidline). This is the sensing region of our device and it is localized tothe rim of the toroid, according to an illustrative embodiment.

FIG. 4: Block diagram of FLOWER. A small, high-frequency dither is usedto modulate the driving laser frequency.

FIG. 5 schematically illustrates a nanostructure positioning processbased on optical tweezers to position individual nanostructures at therim of a silica microtoroid, which has been previously fabricated on asilicon wafer, according to an illustrative embodiment of the invention.

FIG. 6: Artistic rendering showing how light will be coupled into andout of a microtoroid optical resonator using gold nanoshells (whitedots), according to an illustrative embodiment of the invention. Thedarker particles are unbound particles of interest.

FIG. 7 shows four successive frames showing optical trapping andmanipulation of a polystyrene bead relative to other beads undergoingBrownian motion in the background, according to an illustrativeembodiment of the invention.

FIG. 8 shows four successive frames showing optical trapping andmanipulation of a single 400 nm gold nanoparticle, according to anillustrative embodiment of the invention.

FIG. 9 graphically illustrates experimentally-measured maximummanipulation speeds of 1 μm-diameter polystyrene particles, according toan illustrative embodiment of the invention. The experimentally-measuredmaximum manipulation speeds of 1 μm-diameter polystyrene particles areplotted.

FIG. 10 schematically illustrates a nanomanufactured toroid performancetesting apparatus, according to an illustrative embodiment of theinvention.

FIG. 11: Artistic rendering of a gold nanobowtie (not to scale) bound tothe surface of a microtoroid, according to an illustrative embodiment ofthe invention.

FIG. 12: Schematic illustration of a phased array (or metasurface) thathas been attached to the surface of the microtoroid, according to anillustrative embodiment of the invention.

FIG. 13 schematically illustrates a portable FLOWER apparatus, accordingto an illustrative embodiment of the invention.

DETAILED DESCRIPTION OF NON-LIMITING, EXEMPLARY EMBODIMENTS

We disclose herein, among other things, an ultra-sensitive and portable(self-contained), optical resonator-based sensor and thenano-manufacturing of an ultra-sensitive and portable (self-contained),optical resonator-based sensor having one or more nanoparticles disposedon the surface of the optical resonator with precise positioning (towithin ±0.5-100 nm depending on nanoparticle dimensions).

Metal (plasmonic) nanostructures have been shown to generate locallyenhanced electric fields due to surface plasmon excitation whenilluminated with light from the far-field. According to an aspect, weprecisely position and fix one or more plasmonic nanostructures intargeted locations on the surface of a microtoroid optical resonator.This may be accomplished using optical tweezers. Thereafter, we observe“hotspots” of ultra-high electric field intensities (E_(w/nano)=10× to1000× E_(w/o nano)) created within the evanescent zone of themicrotoroid as illustrated in FIG. 3.

Other photonic resonator geometries may be used such as microspheres,bubbles, linear Fabry-Perot, bottles, droplets, cylindrical capillaries,disks, and rings, as well as alternative positioning and attachmentmethodologies including but not limited to atomic force microscopy andmicronozzle deposition as are known in the art.

We previously developed a biosensing technique known as FLOWER(frequency locked optical evanescent resonator; US 2015/0301034) thatuses frequency-locked microtoroid optical resonators to detect singleunlabeled macromolecules. FLOWER has been shown capable of detectingunlabeled single human-interleukin-2 molecules that have a mass of 0.002attograms. In addition to being more sensitive, FLOWER eliminates theneed to label the target molecule, thus providing a reduction in thecomplexity and cost when compared to other assays such as anenzyme-linked immunosorbent assay (ELISA). As illustrated in FIG. 4, thedither signal, when multiplied by the toroid output and time-averagedgenerates an error signal whose amplitude is proportional to thedifference between the current laser frequency and resonant frequency.This error signal is sent to a PID controller, whose output is used toset the laser frequency, thus completing the feedback loop. A computerrecords the observed frequency shifts.

An exemplary embodiment of the invention is a miniaturized FLOWERapparatus 200 that is part of a self-contained, compact, portabledevice, which is able, for example, to be used in the field to quicklydiagnose and establish the prognosis of various diseases. FIG. 13schematically illustrates a portable FLOWER apparatus 200, according toan illustrative embodiment of the invention. Light 203 _(in) is focusedfrom the far-field (laser 201) by a lens 202 onto a nano-antenna 205that has been positioned on the surface of a microtoroid 206. Theback-scattered light 203 _(out) from the antenna is sent to a balanceddetector 209. An injection port 211 is located on the side of thechassis to enable sample delivery into fluidic chamber 215. In theinventive embodiments, the optical fiber used to evanescently couplelight into and out the device is replaced with a more compact and robustsolution, resulting in a device with higher sensitivity and capable ofdetecting smaller molecules such as insulin, or smaller signal changesthat arise as a protein changes conformation. We incorporatenanomaterials, advantageously plasmonic nanoparticles, into the systemto make it more readily manufacturable. The nanoparticles may includenanoshells, gold nanospheres, silver nanospheres, nanorods, nanoplates,nano-bowties, and metal-dielectric composite nanoshells.

While past work has reported the use of gold nanoshells and nanorodswith microsphere resonators to create sensing hotspots, these particleshave been positioned randomly. Furthermore, they have only been used assensing hot spots, and not as a means to effectively couple light intoand out of the devices. The random positioning is also non-ideal forsensing purposes because the effectiveness of a plasmonic hot spotdepends sensitively on which part of the optical resonator the plasmonicparticle is located; the ideal location is at the equatorial regionwhere the evanescent field is greatest (see FIG. 3). Thus, arandomly-positioned particle is likely to generate observed detectionsignals that are lower in amplitude and higher in noise than foroptimally positioned particles as embodied herein.

In the embodied invention, instead of the random placement that has beenused previously, we propose precise, predetermined placement of thesestructures through nanomanufacturing, maximizing the number of thesestructures that can be placed on our sensor as well as optimizing theirpositioning, thereby maximizing our effective sensor capture area. Inaddition, the embodied approach allows us to control the orientation ofthese structures, which allows us to align their direction of maximumpolarizability with the polarization of the light orbiting in theoptical resonator, in the case where the nanostructures arenonspherical. This alignment maximizes the electric field enhancementprovided by the nanostructures. Finally, we can localize nanostructuresat known positions on the resonator surface to interface with far-fieldmicro-optical elements to launch light into the resonator, as well as toread out a signal, side-stepping the cumbersome nature of coupling tothe resonator with a tapered optical fiber (FIG. 1) as known in the art.

A microtoroid optical resonator 206 as shown in FIG. 2A can function asan extremely sensitive sensor. More particularly, it may function aslabel-free sensor that can detect the presence of particles or moleculesby measuring small refractive index changes without the need forfluorescent or radioactive tagging of the target of interest.

Microtoroid optical resonators operate on the principle of resonantrecirculation of light. They are the optical analog of an acousticwhispering gallery, first described by Lord Rayleigh. He reportedlystood under the dome of St. Paul's Cathedral in London and noticed thatwhispers at one end of the dome could be heard 40 meters away at theother end of the dome as sound skirts along the edges with negligibleloss. Optical resonators operate under the same physical principle basedon light instead of sound.

Light is evanescently coupled into these devices (as known) and iscontinuously totally internally reflected within them, generating anevanescent field 220 as illustrated in FIG. 2B and by the solid curvedline 220 in FIG. 3. When a particle 218 having a different refractiveindex (or polarizability) than the background medium enters theevanescent field 220, part of the light enters the particle, changingthe optical path length of the light and decreasing the frequency atwhich the toroid resonates. This enables sensitive monitoring ofparticle binding events as illustrated in FIG. 2C. Because lightcirculates multiple times within the device before exiting, it interactsmultiple times with a particle, making the microtoroid a more sensitivesensor than a traditional single-pass device such as a waveguide orcuvette. More traditional optical resonators such as microrings havedemonstrated picomolar sensitivities of proteins but have not been ableto detect single molecules. Microspheres have reportedly been showncapable of detecting single Influenza A virus particles but not singleprotein molecules. Recently, researchers have adhered gold nanoshellsand nanorods to the surface of microspheres to create smallplasmonic-enhanced sensing hotspots for detecting proteins and DNA. Amicrotoroid geometry appears to be the most advantageous choice tooptimize sensitivity to the smallest possible particles.

According to an embodied method, we use optical tweezers to preciselyposition nanostructures (e.g., gold spherical and bowtie-shaped) on thesensing region (rim) of a silica microtoroid which has been previouslyfabricated on a silicon wafer as illustrated in FIG. 5. A microfluidicchamber 500 was constructed around the microtoroid 506 with an inlet 511and an outlet (not shown), each located far away (on the order ofmillimeters) from the microtoroid. Nanostructures 505 were suspended ina fluid 521 and introduced into the microfluidic chamber through, e.g.,a manual syringe, syringe pump, microfluidic flow controller, orcapillary action (not shown). The inlet was located far enough away fromthe microtoroid such that it is statistically improbable fornanoparticles that enter the microfluidic channel to encounter themicrotoroid via diffusion alone. Chemical interactions (described hereinbelow) fix the nanostructures in place on the microtoroid, as furtherillustrated in FIG. 6. When illuminated with light, these structureshave demonstrated enhanced electric fields, E_(w), of up to 1000× in thecase of a nanobowtie.

Out of a wide range of potential plasmonic materials, such as goldnanospheres, silver nanospheres, nanorods, nanoplates, nanobowties, ormetal-dielectric composite nanoshells, we initially used simplespherical gold nanospheres with a diameter of 50 nm. Although theplasmon resonance of these particles (peak at λ=528 nm) did notprecisely match the operating range of our current tunable laser system(632.5 nm<λ<637 nm), the plasmon resonance of the particles is broad andsome of the plasmon resonance tail extends into the wavelength range ofthe laser system, making coupling feasible. Even when the nanoparticleis not resonant at the excitation wavelength, non-resonant oscillationswill still occur and which can be used to couple light into themicrotoroid as well as amplify biosensing. Simple gold nanospheres ofthis size can be optically trapped using a conventional high-NAfocused-beam optical tweezer. It is likely that many of the other typesof nanomaterials may also be feasibly trapped; however nonsphericalparticles have non-isotropic polarizabilities that can complicate andpotentially disrupt the optical trap. We explore some of these moreexotic nanoparticle shapes, in the form of pairs of triangularnano-plates aligned to form a nanobowtie 505 a (FIG. 11).

As mentioned herein above, the nanospheres serve two purposes: (1) tocouple light into and out of the microtoroid (FIG. 6) and eliminate theneed for an optical fiber, and (2) to serve as a sensing hotspot forbiological/chemical molecules. We performed finite element simulations,as described below, in order to determine the maximum number of goldnanospheres that we can place around the rim of the microtoroid whilestill maintaining quality (Q) factors of our device above 10⁵. Q is ameasure of the energy storage capabilities of a resonator and is definedas Δλ/λ, where is the center wavelength of the resonance peak and Δλ, isthe full width of the peak at half of the maximum value. Excessivenumbers of gold nanospheres can lead to excessive scattering loss, whichwill eventually degrade the Q of microtoroid. In this way the use ofthese plasmonic particles is a “two-edged sword;” i.e., efficientcoupling enables the whispering gallery mode to be efficiently launchedinto the device and read out, while at the same time leads to scatteringlosses. On the other hand, the more nanospheres that can be preciselypositioned around the rim of the toroid, the more sensing hotspots thatare created. We also used simulation to investigate the effect ofnanoparticle size on coupling efficiency and optimizing this balance.

Full-wave electromagnetic simulations of the microtoroidal resonatorwere performed using COMSOL and MEEP. MEEP is an open-source softwarepackage developed at the Massachusetts Institute of Technology (MIT). Wemodeled surface roughness, material absorption, and nonlinearities.

In parallel to designing the precise locations and optimum number ofnanoparticles to adhere to the toroid, we developed techniques toprecisely position and bind nanoparticles to highly curved silicastructures like microtoroids. The embodied manufacturing methodsincorporate various optical traps whose performance determines themaximum speed with which particles can be adhered to the microtoroids,which will limit the rate of manufacturing of such devices, as well aspositioning accuracy, which limits the manufacturing precisiontolerance.

These manufacturing parameters were quantified using our availableoptical trapping system. The key elements of the system include: (1) a30 W continuous-wave laser operating at λ=1064 nm wavelength with highpower stability (<2% variation) and mode quality M²<1.1; (2) a 100×/1.1NA water immersion microscope objective corrected into the infrared witha cover glass correction collar; and (3) a nanopositioning stage with 1nm resolution, total travel distance of 26 mm, <1 nm repeatability (overa reduced 100 μm travel distance), and maximum speed of 20 mm/s. FIG. 7shows four successive frames showing optical trapping and manipulationof a polystyrene bead 701 relative to other beads undergoing Brownianmotion in the background. A single bead is trapped in the center of thefield of view. Here, the optical trap and microscope visualization arein a fixed reference frame, while the substrate and background beadsexhibit the relative motion of a computer-controlled translation stage.

Beyond this simple demonstration of conventional optical trapping, wehave also verified that we can trap metallic particles. FIG. 8 showsfour successive frames showing optical trapping and manipulation of asingle 400 nm gold nanoparticle 801. A single 400 nm gold particle istrapped in the center of the field of view. Four successive frames showthis particle being manipulated relative to a freely-floating particlein the background. In this experiment, the optical trap and microscopevisualization are in a fixed reference frame, while the substrate andbackground beads exhibit the relative motion of the computer-controlledtranslation stage. While in general metals have very different opticalproperties from dielectrics, spherical nanoparticles of both materialscan be optically trapped via the same mechanism as long as the particlesize is significantly smaller than the wavelength of the trapping beam.In fact, because of the enhanced polarizability of metals relative todielectrics, they are trapped more easily. The governing equation foroptical trapping gradient force (lateral force) for particlessignificantly smaller than the wavelength (Rayleigh particles) is

$\begin{matrix}{{F_{grad} = {\frac{{Re}\left\{ \alpha \right\}}{2}{\nabla\left\langle {E}^{2} \right\rangle}}},} & (1)\end{matrix}$

where

|E|²

is the time-averaged magnitude-squared of the electric field and α isthe complex polarizability of the particle, given by theClausius-Mossotti relation,

$\begin{matrix}{{\alpha = {V_{p}\frac{\epsilon_{p} - \epsilon_{w}}{\epsilon_{p} + {2\epsilon_{w}}}3\epsilon_{0}}},} & (2)\end{matrix}$

where v_(P) is the particle volume, ∈_(p) is the dielectric constant ofthe particle, ∈_(w) is the dielectric constant of the surrounding water,and ∈_(D) is the free-space permittivity. For a 50 nm diameter silicaparticle, Re{α}≈1.0×1.0⁻³⁴ Cm²V⁻¹, while for the same size of goldparticle Re{a}≈2.0×10⁻³³ cm²V⁻¹. This translates into the goldnanoparticle being approximately 20 times easer to trap than the silicananoparticle, and both particles can be trapped at the focus of atightly-focused laser beam.

In addition to gradient forces, another type of force called thescattering force is important in trapping particles in the z-direction.As a result, the trap in the z-direction tends to be weaker than in thetransverse directions, however we do not expect this to significantlyimpact our approach because the time-limiting step from a manufacturingpoint of view will be the time it takes to drag a particle transverselytoward the optical resonator.

The strength of the optical trapping force directly affects the maximumparticle manipulation speed. The maximum manipulation speed is importantas it can limit the speed with which nanostructures can be brought tothe microtoroid. Before measuring manipulation speeds for nano-scaleparticles, we have started with polystyrene particles of diameter D=1μm, whose results are shown in FIG. 9. These particles can be reliablymanipulated at speeds as large as 0.2 mm/s in our system, withouttweaking or optimizing the trapping beam. Theoretically, the maximummanipulation speed, v_(max), is governed by the force balance betweenthe optical trap and the Stokes' drag force of the particle movingthrough the liquid. This balance implies

$\begin{matrix}{{v_{\max} = \frac{F_{{grad},\max}}{3{\pi\mu}\; D}},} & (3)\end{matrix}$

where F_(grad,max) is the maximum gradient force exerted by the opticaltrap, and μ is the viscosity of the surrounding medium (water). Webelieve that the current maximum manipulation speed of 0.2 mm/s for 1 μmpolystyrene spheres can be significantly improved. Combining Eqs. (1)and (3), F_(grad) is proportional to laser beam power, and thus v_(max)is proportional to laser beam power. This expected linear relationshipis in contrast to that shown in FIG. 9, where a nonlinear dependence isobserved, which may be due to hydrodynamic effects from the nearby wallsof the chamber, or may be due to vibrations in the translation stagethat scale with speed. In these tests, we have currently only used 3% ofthe maximum power of the laser beam. We expect further improvements tothe maximum manipulation speed through modifying the filling fraction ofthe objective, adjusting the polarization state of the laser beam, andthrough fine tuning the correction collar and divergence of the incominglaser beam.

We expect to be able to trap gold nanoparticles with diameters as smallas 18 nm. A general rule of thumb is that a stable trap requires apotential well depth of W<10 kT, where k is Boltzmann's constant, and Tis the temperature. The potential well depth can be calculated using Eq.(1), and the equation,

$\begin{matrix}{{W = {{- {\underset{- \infty}{\int\limits^{0}}{{F_{grad} \cdot \hat{x}}{dx}}}} \propto {{Re}\left\{ \alpha \right\}}}},} & (4)\end{matrix}$

We would thus expect to be able to trap any type of particle with Re{α}greater than that of the 18 nm gold particle. From Eq. (2), this wouldcorrespond to polystyrene particles as small as 39 nm, and silicaparticles as small as 49 nm. These values are based on the same trappingpower as used in Hansen et al., Expanding the optical trapping range ofgold nanoparticles. Nano Lett. 5, 1937-1942 (2005); however, since wecan use higher laser power, we expect to be able to trap even smallerparticles.

The strength of the trap also affects the accuracy with which particlescan be positioned, or in other words the ability of the trap to opposeBrownian motion, as derived below. If we assume the profile of ourfocused beam is Gaussian, then its complex electric field is

$\begin{matrix}{{{E(r)} = {{Re}\left\{ {E_{0}e^{- \frac{r^{2}}{w^{2}}}e^{{- i}\;\omega\; t}} \right\}}},} & (5)\end{matrix}$

where w=FWM/√{square root over (4 ln 2)} defines the spot size in termsof the beam's full width at half-maximum (FWHM), ω is the frequency ofthe light, and t is time. The optical trap is analogous to a spring-masssystem with an effective spring constant

$\begin{matrix}{{{K = {- \frac{\partial F}{\partial r}}}}_{r = 0}.} & (6)\end{matrix}$

Combining Eqs. (1), (5), and (6), the resulting spring constant is,K=Re{α}E₀ ²/w². The positional accuracy of the trap is governed by theexpected value of the radial position of the bead due to thermal forces,calculated using Boltzmann statistics

$\begin{matrix}{\left\langle r \right\rangle = {\sqrt{\frac{\pi\;{kT}}{2K}}.}} & (7)\end{matrix}$

Let us assume that we have an optical trap with a spot size FWHM=λ/2=532nm that can trap an 18 nm gold nanoparticle with 10 kT potential welldepth. This combination of parameters represents the worst case in termsof positional accuracy. The potential well depth, in concert with Eqs.(4) and (5), can be used to infer a value of E₀, which in turn providesa value of

r

=60 nm. While this positional accuracy would likely make the techniqueinfeasible for particles this small, it turns out that

r

∝D^(−3/2), and therefore larger particles exhibit acceptable positionalaccuracies of

r

=¹³ nm for a 50 nm diameter gold particle, and

r

=nm for a 100 nm gold particle. These values of

r

provide more than sufficient accuracy to optimally locate nanoparticlesin the evanescent zone of the microtoroid. It should also be emphasizedthat our platform has a stronger laser than that used in Hansen, id.,and thus we expect even better positional accuracies than the valuesquoted here. While external disturbances, vibrations, etc. can alsoimpact positional accuracy, these effects can be mitigated usingvibration-isolated optical tables and other engineering controlmeasures.

FIG. 10 schematically illustrates a nanomanufactured toroid performancetesting apparatus 1000, according to an illustrative embodiment of theinvention. A tunable laser 1001 is focused using a standard microscopeobjective 1002 onto a specific nanostructure 1005 a on the rim of themicrotoroid 1006 to generate a whispering gallery mode inside thetoroid. Readout is performed by imaging a nanostructure 1005 b that isdiametrically opposed to the in-coupling nanostructure onto the activearea of a balanced photodetector 1010. The rest of the testing apparatusis the same as that depicted in the block diagram in FIG. 4.

In order to fix the gold nanoparticles in precise positions on themicrotoroid's rim, we covalently bind a silane-PEG-biotin linker to thesurface. The gold nanoparticle is coated with streptavidin, which allowsfor strong binding to the biotin linker. The streptavidin coating on thenanoparticles will also be helpful in functionalizing thesenanoparticles to specifically capture target analyte molecules forsensing. We will confirm the presence and location of the goldnanoparticles using scanning electron microscopy (SEM).

Other than biotin-avidin interactions, there are many other bindingmechanisms that may be used. These include antigen-antibodyinteractions, the binding of complimentary DNA oligomers, as well asphysical interactions such as electrostatic, Van der Waals, steric, andcovalent bonding. These types of interactions may be used to bindnanoparticles to the surface of the toroid, as well as to bind one ormore linkers to the nanoparticle(s) and/or toroid to facilitate theirlinkage.

In addition to using single nanoparticles to couple light into and outof the optical resonator, we also propose to use phased arrays ofnanoparticles 1202 as illustrated in FIG. 12. These phased arrays can beused to provide more directional and enhanced coupling both into andout-of the optical resonator. These arrays can function similarly to,for example, Yagi-Uda antennas, which are widely adopted for the receiptof broadcast television signals. Beyond improving coupling efficiency,such antenna-like arrays can also directly aid in analyte sensing. FIG.12 schematically illustrates a phased array (or metasurface) that hasbeen attached to the surface of the microtoroid. The phased arrayconsists of nanoparticles whose sizes, shapes, compositions,orientations, and positions have been carefully chosen to couple lightinto the toroid. Similar principles can be used to couple light out ofthe toroid, or fabricate signal-enhancing nanostructures.

It is also possible to use complex assemblies of particles that functionas a single entity, similar to a nanophotonic device based on theconcept of photonic metamaterials. This device can be optimized totransduce far-field radiation with electromagnetic near-fields. A phasedarray can be considered as one such type of complex particle assembly,although highly compact nanoparticle arrays are likely better consideredin terms of a metamaterial conceptual framework instead of aphased-array conceptual framework (FIG. 12).

We will test the performance of the coupled resonator in two phases:first without any target analyte, and second, in the presence of targetanalytes. These two phases will allow us to separately understand thephysical properties and the chemical properties of the nanomanufactureddevice. In the first phase, we will evaluate the performance of thedevice by experimentally measuring its Q-factor and comparing it tosimulations. Our experimental approach to measuring Q-factor is depictedin FIG. 13. We will couple light into the device by positioning one ofthe attached gold nanoparticles at the focus of a microscope objective(NA>0.5), and sending collimated laser light into the objective, so thatit focuses on the nanoparticle. This focused light will excite plasmonicoscillations of the nanoparticle. These plasmonic oscillations willevanescently couple into the microtoroid optical resonator, generating acirculating mode of light within the resonator. This circulating modewill be strongly amplified when the frequency of the incident laserlight matches the resonant frequency of the microtoroid-nanospheressystem of coupled oscillators.

The degree of amplification will be tracked by imaging the scatteringfrom another nanostructure. This scattered light will be collected outof our device with the same objective with a beamsplitter 223 placedbehind the objective to direct the light to an auto-balancedphoto-receiver 209 (FIG. 12). Because the in-coupling nanoparticle 205 ais significantly separated in space from the out-coupling nanoparticle205 b, it is possible to spatially resolve these two points in theimage-space of the objective and make sure that simple back-scatteringfrom the in-coupling nanoparticle is not collected by the auto-balancedphoto-receiver. The degree of amplification as a function of thewavelength of the tunable laser source will be used to measure thelinewidth of the resonances of the coupled microtoroid-nanostructuresystem. Measuring these linewidths is equivalent to measuring theQ-factor of the system.

We will also quantify the frequency shifts that occur when targetanalytes bind to the device, as well as quantifying the signal-to-noisewith which we can measure these shifts. Target molecules will becaptured using biotinylated antibodies, which will have been previouslybound to the streptavidin-coated gold nanoparticles. The shift inresonance will be detected by monitoring the same out-couplingnanoparticle that was previously used to measure the device Q-factor.

To further miniaturize this device, we will replace the microscopeobjective with a small lens to make the system more compact andcost-effective. For this application, it is not necessary to have asuper-high numerical aperture lens (spot sizes of ˜10 μm would besufficient), and aberrations can be tolerated. Eliminating the opticalfiber reduces the precision with which the toroid needs to be positionedrelative to the optical delivery system (now far-field lenses), andthereby the major roadblock in the path toward mass-producible andportable sensors based on this technology. By moving to lower qualitycoupling optics, it is likely that there may be some decrease in SNR,which we will measure experimentally.

The first analyte we will test are 20 nm diameter biotin-coatedpolystyrene beads, which are expected to bind to the surface ofstreptavidin-coated gold nanospheres that we previously adhered to thesurface of the toroid in our nanomanufacturing step. We will measure thechange in resonance frequency, and compare the observed value to thatobserved when polystyrene beads bind directly to a portion of the toroidwithout a nanoshell (these latter results are from ourpreviously-published data. The change in resonance frequency will bemonitored over time using the output of the photodiode. For a particlebinding to a bare resonator, the shift upon binding of a particle isgiven by:

$\begin{matrix}{{d = {{2a} = {2\left( \frac{2V_{m}E_{0,\max}^{2}}{{DE}_{0}^{2}\left( r_{s} \right)} \right)^{1/3}\left( \frac{\Delta\lambda}{\lambda} \right)^{1/3}}}},} & (8)\end{matrix}$

where d is the diameter of a bound particle, α is the radius, V_(m) isthe electromagnetic mode volume of the microtoroid, D is a dielectricfactor calculated from the index of refraction of the bound particle andthe background solution, E₀, max² is the electric field intensity at themicrotoroid equator, and E₀ ²(r_(s)) is the intensity of the electricfield at the microtoroid surface. V_(m) and E_(0,max) ²/E₀ ²(r_(s)) aredetermined from finite element simulations.

We will proceed to test progressively smaller analytes to determine theminimum particle/molecule size that can be detected by this coupledsystem. It is expected that the minimum particle size will besignificantly smaller than for the bare toroid. For each particle size,we will quantify the SNR of the detection process.

Once we demonstrate successfully coupling light into and out of ourdevice using nanospheres, we will progress to positioning a morecomplicated nanobowtie structure on the rim of a microtoroid. FIG. 11 isan artistic rendering of a gold nanobowtie 505 a (not to scale) bound tothe surface of a microtoroid. Gold nanobowties have been shown to have a1000× electric field enhancement at the center of the bowtie. Thiselectric field enhancement will cause in corresponding increase in thesignal to noise ratio of the device. We will manufacture gold bowties byusing commercially available gold nanotriangles ˜50 nm in height, andindependently position them so that their relative spacing is 10-20nanometers apart based on the precision of the optical tweezers aroundthe rim of the microtoroid. 50 nm is chosen as it should be able to beeasily trapped via optical tweezers. The spacing between the triangleswill be made as small as possible, within the placement precision of theoptical tweezers, which we estimate to be ˜10 nm. To determine how manygold nanotriangles we will need and how far apart they should be spaced(pitch) we will first perform electromagnetic simulations, again usingCOMSOL and MEEP.

We will fix the nanobowties to the surface of the microtoroid usingstrepavidin-biotin coupling. In this procedure we will functionalize thetoroid surface using a silane-PEG-biotin molecule. The goldnanotriangles will be functionalized with thiol-PEG-biotin molecules,and subsequently coated with free streptavidin molecules. Thesestreptavidin molecules coating the gold triangles will thenspontaneously bind to the biotinylated microtoroid surface. We will holdthe gold triangles with our optical tweezers until they firmly adhere tothe surface. The presence of the nanobowties will be confirmed via SEM,and the gap spacing will be measured, which is a critical parameter inthe degree of plasmonic enhancement that these structures can supply.

In addition to our numerical simulations using COMSOL and MEEP, we willexperimentally measure the signal enhancement provided by thenanobowties by binding a 20 nm polystyrene bead to the center of thebowtie and comparing this to the previous signal shift observed from 20nm polystyrene beads binding to a bare resonator, as well as by testingsmaller molecules.

The metal nanostructures may be used, with particular advantage, for (1)optimized sensing hotspots and (2) as a means to couple light into andout of the optical resonators without the need for an externalwaveguide, as is known in the art. The embodied devices mayadvantageously be applicable as extremely sensitive and portablebiological and chemical sensors, as well as in silicon photonics forcomputing and communications. In communications, optical resonators canbe used for wavelength division multiplexing and switching/routing ofoptical signals. The embodied invention provides a new way of couplingto these resonators in these applications. Other non-limitingapplications include second harmonic generation and surface enhancedRaman scattering, which both benefit from an enhanced interaction oflight with matter. In these applications, the combination of ananoparticle with an optical microresonator leads to a hot-spot in theelectric field intensity that can greatly enhance second harmonicgeneration and surface-enhanced Raman scattering because these processesscale nonlinearly (exponent>1) with electric field intensity.

1.-22. (canceled)
 23. An optical apparatus, comprising: a non-planarwhispering gallery mode optical resonator including one or morenanoparticles disposed on a surface of the resonator at respective,pre-determined locations, wherein the surface of the resonator exhibitsa finite radius of curvature in at least two orthogonal directions;wherein the nanoparticles are configured for optical coupling into andout of the resonator and the resonator is a sensor.
 24. The opticalapparatus of claim 23, wherein the one or more nanoparticles arenon-spherical.
 25. The optical apparatus of claim 24, wherein the one ormore non-spherical nanoparticles have an orientation that is alignedwith a polarization of light propagating in the optical resonator. 26.The optical apparatus of claim 24, wherein the one or more non-sphericalnanoparticles have a bow-tie geometry.
 27. The optical apparatus ofclaim 23, wherein at least two the nanoparticles are disposeddiametrically opposed on an equatorial region of a microtoroidresonator.
 28. The optical apparatus of claim 23, wherein the one ormore nanoparticles are chemically attached to the microtoroid.
 29. Theoptical apparatus of claim 23, wherein the one or more nanoparticlescomprise a phased array of nanoparticles.
 30. The optical apparatus ofclaim 23, wherein the one or more nanoparticles comprise one or moregroupings of nanoparticles.
 31. The optical apparatus of claim 23,wherein the one or more nanoparticles comprise an assembly ofnanoparticles.
 32. The optical apparatus of claim 23, wherein theoptical resonator is characterized by a quality factor, Q, that is equalto or greater than 10⁵.
 33. An optical apparatus for detecting at leastone molecule in a sample, comprising: a substrate; a whispering gallerymode optical resonator comprising a curved resonance portion, saidwhispering gallery mode optical resonator being at least one of attachedto, or integral with, said substrate such that said curved resonanceportion is away from and without contacting said substrate, wherein saidcurved resonance portion has an outermost rim; and a first nanoparticleattached at a position on said outermost rim of said curved resonanceportion of said whispering gallery mode optical resonator, wherein saidfirst nanoparticle has a structure and composition to facilitatecoupling light at least one of into or out of said curved resonanceportion of said whispering gallery mode optical resonator.
 34. Theoptical apparatus according to claim 33, further comprising a secondnanoparticle attached at a second position on said outermost rim of saidcurved resonance portion of said whispering gallery mode opticalresonator, wherein said second nanoparticle has a structure andcomposition to facilitate coupling light at least one of into or out ofsaid curved resonance portion of said whispering gallery mode opticalresonator, and wherein said whispering gallery mode optical resonator ischaracterized by a quality factor, Q, that is equal to or greater than10⁵.
 35. The optical apparatus according to claim 34, furthercomprising: an optical source arranged to illuminate at least one ofsaid first and second nanoparticles to provide enhanced optical couplinginto said whispering gallery mode optical resonator; and an opticaldetector arranged to receive light coupled out of said whisperinggallery mode optical resonator by at least one of said first and secondnanoparticles to provide enhanced outcoupling, wherein said opticaldetector is further configured to distinguish light coupled out of saidwhispering gallery mode optical resonator from illumination light thatis at least one of scattered from or reflected from said whisperinggallery mode optical resonator or said first or second nanoparticles.36. A method of producing an optical apparatus, comprising: providing asubstrate; forming a whispering gallery mode optical resonator at leastone of from, integral with or attached to said substrate, saidwhispering gallery mode optical resonator comprising a curved resonanceportion and is attached to said substrate such that said curvedresonance portion is away from and without contacting said substrate;and attaching a first nanoparticle substantially at a preselectedposition on said curved resonance portion of said whispering gallerymode optical resonator, wherein said first nanoparticle has a structureand composition to facilitate coupling light at least one of into or outof said curved resonance portion of said whispering gallery mode opticalresonator.
 37. The method according to claim 36, wherein said attachingsaid first nanoparticle uses optical tweezers to position said firstnanoparticle at said preselected position on said curved resonanceportion of said whispering gallery mode optical resonator to within apreselected tolerance.